Magnetic mass spectrometer with shaped, uniformly saturating magnetic poles

ABSTRACT

A magnetic mass spectrometer having a magnetic analyzing sector utilizing shaped magnet poles of a specific configuration so as to produce uniform magnetization of the pole material and constant flux distribution at all magnetic field strengths. The magnet poles are shaped such that the surfaces thereof conform to an exponential function. Magnetic shunts are located at a predetermined spacing from the entrance and exit end of the analyzing sector to locate the magnetic field boundary.

United States Patent Hull et al.

[451 Jan. 22, 1974 MAGNETIC MASS SPECTROMETER WITH SHAPED, UNIFORMLY SATURATING MAGNETIC POLES [75] Inventors: Charles W. Hull, Sierre Madre;

- Charles R. McKinney, Monrovia,

both of Calif.

[7 3] Assignee: Bell 8!. Howell Company, Chicago,

Ill.

[22] Filed: July 17, 1972 21 Appl. No.: 272,647

Related US. Application Data [62] Division of Ser. No. 15,186, Feb. 27, 1970, Pat. No.

[52] US. Cl. 335/210, 250/419 [51] Int. Cl. H0lf 7/00 [58] Field of Search 335/210, 211; 250/419 [56] References Cited UNITED STATES PATENTS 3,197,678 7/1965 Primas 250/419 ME 3,487,208 12/1969 Futrell et a1. 250/419 ME Primary Examiner-George Harris [5 7] ABSTRACT 6 Claims, 10 Drawing Figures 82 {in 25a 25 This is a division, of application Ser. No. 15,186, filed Feb. 27, 1970, now US. Pat. No. 3,699,332.

DESCRIPTION OF THE PRIOR ART The present invention relates to magnetic momentum analyzers and in particular to positive ion mass spectrometers. Prior to relatively recent developments in the art, magnetic momentum analyzers have been characterized by a magnetic analyzing sector having poles with precise, sharply defined, usually square, pole faces.

The use of shaped, non-square pole pieces in magnetic momentum analyzers has been proposed as a way in which to combat distortions in the magnet flux distribution in the pole pieces andunpredictable aberrations in particle trajectory encountered by charged particles particularly at the entrance and exit ends of the magnet in such analyzers due to edge effects in the magnetic material. Specifically, a curvilinear shape corresponding to an exponential function first postulated for electric field generating electrodes has been proposed for the end and side faces of the pole pieces. The result of using such a shape is that magnetization of the magnetic material is uniform throughout material for all field strengths and without distortion particularly near the edges and corners of the pole pieces regardless of the magnetization level of the material. Such uniform magnetization means constant flux distribution at all field strengths and the elimination of end effects at saturation levels. In one instance the importance of this discovery has been recognized and utilized in a magnetic beam analyzer for measurement of the energy of nuclear particles to a heretofore unattainable degree of accuracy. As used in connection with the present discussion, the term uniform magnetization refers to the property of the magneticmaterial wherein the flux distribution of the magnetic field remains constant and uniform at all field strengths. This characteristic is also sometimes referred to as one in which the magnetic field saturates in a uniform manner.

In one specific version of exponentially shaped pole pieces the end and side edges adjacent the pole faces are rounded on a circular radius having a dimension which is a predetermined fraction (0.83) of the actual spacing between the pole pieces, i.e., the width of the magnetic gap. In addition, the end and side faces extending away from the rounded edges are provided with an outward taper relative to the pole faces, which taper forms an angle of approximately 5.7 with respect to a line erected perpendicularly to the pole face. Upon analysis, however, it has been found that the resultant pole shape obtained using these parameters is a poor approximation of the true theoretical exponential shape and that as a result distortion and nonuniformities of the magnetic field are still experienced.

To further improve the operation of charged particle analyzers, the use of field clamps, also called magnetic shunts, adjacent the end faces of analyzing sector magnets has also been proposed. The function of such shunts is to aid in producing a sharp cutoff between the region of zero field externally of the magnet and the region of magnetic field within the magnet. Such shunts also have the effect of eliminating the reversal of the magnetic field which often occurs in magnets at a distance removed from the magnetic gap.

The spacing of these shunts relative to the end faces of the magnet particularly with exponentially shaped poles has usually been established at a distance equal to the spacing between the pole pieces. Such spacing, however, has been found to result in a loading of the poles producing an edge effect like phenomenon at the end faces of the magnet which reintroduces distortions and thereby prevents design of an instrument of accurately predictable performance. While the benefits of utilizing exponentially shaped magnetic poles in charged particle analyzers have been recognized, at least to a limited degree, their application has been limited to use with energy analyzers. Thus, in general, instruments utilizing such magnets have been confined to use with particles of known mass or derivation.

SUMMARY OF THE PRESENT INVENTION A new shape for the pole pieces and a new spacing for the magnetic shunts are provided by the present invention. In providing a new shape for the pole pieces, an accurate reproduction of the true theoretical exponential shape for the ends and sides of the pole pieces is accomplished with the resultant improvement in the uniformity of the flux distribution. At the same time, a considerably greater spacing is provided for the shunts than has heretofore been provided in prior art arrangements which reduces the loading effect due to the shunts to a negligible amount while retaining the benefit of precisely locating the magnetic field boundary.

A new magnetic mass spectrometer utilizing a magnet according to the present invention, one which operates on either the single or double focusing principle and having substantially improved operating characteristics is also provided. Inherent in the use of exponentially shaped poles in a variable magnetic field, double focusing mass spectrometer is the recognition that such an instrument possesses a fixed focal point and in conjunction with an electrostatic analyzer is capable of first order focus of energy and angular divergence with minimal higher order aberrations.

In one aspect the present invention provides a uniformly saturating magnet comprising a first pole half of a generally U-shaped configuration in both a transverse and longitudinal direction and a second pole half of a generally U-shaped cross-section in both a transverse and longitudinal direction spaced a predetermined distance from the first pole half. The two pole halves are aligned with the base portions of their U-shape facing each other in a parallel orientation. The side and end edges of the opposing base portions are rounded on a radius of approximately 1.25 times the distance between the pole halves and the arm portions of the U- shape are provided with an outward taper of a predetermined slope with respect to a perpendicular through the base portions. Electric coil means are also provided in magnetic field generating relation to the pole halves.

In another aspect the present invention provides an improved mass spectrometer comprising a source of ions, a detector of ions and a deflecting and focusing magnetic analyzing sector interposed between the ion source and ion detector along the path of ions from the source. The magnetic analyzing sector includes a pair of shaped pole pieces of a magnetic material, the pole pieces being spaced a predetermined distance apart and having a predetermined thickness and width, the

shaping of the pole pieces being chosen such that the magnetic material magnetizes uniformly and the magnetic flux distribution in the magnetic material remains constant at all magnetic field strenghts. Means for varying the magnetic field in the magnetic analyzing sector for bringing ions of a predetermined mass into register at the detector are also provided.

In terms of ion optics, the elimination of magnetic distortion means that a mass analyzing instrument can now be designed in which all parameters are precisely determinable prior to actual instrument construction. A double focusing mass spectrometer according to the present invention utilizing shaped magnet pole pieces having magnetic shunts spaced at specified distances from the entrance and exit of the magnetic sector and an electrostatic analyzer (spherical or cylindrical) provides an instrument which has a focal point which is fixed with respect to both angular and energy deviations to first order and further one in which higher order aberrations are very small.

In addition to the preceding, a new property of exponentially shaped magnetic poles has been discovered, namely, that such poles have significantly lower magnetic reluctance compared to square poles of comparable size. In terms of operating characteristics this means that a shaped magnet according to the present invention canobtain substantially higher flux levels for a given amount of magnetic material and a given pole spacing in comparison with a magnet having square poles. The increase in flux density plus the elimination of edge effects at the corners of prior art square poles means that the operating range of such a magnet in a typical high resolution mass spectrometer can be doubled from kilogauss to at least kilogauss. Thus, an operator utilizing an instrument according to the present invention can obtain four times the mass range heretofore obtainable or a commensurate increase in resolution due to an ability to use four times the amount of accelerating voltage for an equivalent mass than heretofore possible. A corollary of this newly discovered property is that operating results comparable to a conventional high resolution square pole magnet instrument can now be obtained by means of an instrument utilizing a substantially smaller exponentially shaped magnet.

DESCRIPTION OF THE DRAWINGS The features and advantages of the invention outlined above will be better understood by reference to the following figures in which:

FIG. 1 is a diagram of a single focusing mass spectrometer utilizing the magnet structure of the present invention;

FIG. 2 is a diagram of a double focusing mass spectrometer utilizing the magnet structure of the invention;

FIG. 3 is a plan view of a magnetic analyzing sector utilizing pole pieces according to the present invention; FIG. 4 is a section view taken along line 4-4 of FIG. 3;

FIG. 5 is a section view taken along line 5-5 of FIG.

FIG. 6 is a side elevational view taken along line 6-6 of FIG. 3;

FIG. 7A is a plan view of a shunt plate utilized with the magnetic analyzing sector of the present invention;

FIG. 7B is an elevational view of the shunt plate shown in FIG. 7A;

FIG. 8 is a graph illustrating the operating characteristics of a magnetic analyzing sector according to the prior art and according to the present invention; and r FIG. 9 is a schematic diagram of the pole pieces, core, yoke and electric coils according to the present invention.

DESCRIPTION OF A SPECIFIC EMBODIMENT The present invention specifies the use of shaped pole pieces of a particular configuration as part of the electromagnet utilized in the magnetic momentum analyzer and further specifies an improved double focusing mass spectrometer utilizing such an electromagnet. A shorthand expression for describing pole pieces of the desired configuration is to refer to them as Rowgowski poles. Poles of this type have a geometry in which the edges and faces are shaped such that the outline or profile of such pole pieces follow or closely approximate an exponential function defined by a set of equations (see below) first proposed by W. Rowgowski for electric field generating electrodes. (Archiv fur Elecktro-technik, Vol. 12, 1923, pp. l-l9).

While the applicability of the Rowgowski equations to pole pieces of electromagnets has been suggested previously, their use in magnetic momentum analyzers has been limited to instruments which are utilized in a fixed focus mode to make energy measurements of particles of a known mass. The present invention specifies the provision of Rowgowski poles in positive ion mass spectrometers utilizing variable magnetic fields to produce a focus at a fixed point with respect to the exit end of the magnetic analyzing sector for ions of all masses. In addition, the shaped poles according to the present invention have an altered profile relative to prior art Rowgowski poles which produces a significantly more accurate approximation of the exponential functions defined by the Rowgowski equations.

The application of the invention to a single focusing mass spectrometer is shown in FIG. 1. In that figure a source of ions 10 is disposed at a point removed from a deflecting and focusing magnet in sector 12 according to the present invention and a detector 14 is located at a point removed from the exit end of the magnet and positioned at the focal point 16 of the magnet. Suitable electronics 18 are connected to detector 14 for providing the desired readout of the conditions at the detector, for example, the magnitude of the ion current incident thereon. A typical magnetic sector (FIG. 9) according to the present invention comprises a pair of electromagnetic coils 13 disposed in magnetic field generating relation to a pair of cores l5 and a pair of opposed, shaped pole pieces 17 of the Rowgowski exponential configuration. A yoke 19 completes the magnetic circuit between the cores and pole pieces. It is to be understood throughout the discussion of the present disclosure the indication that the pole pieces are of an exponential shape refers to a shape defined by the Rowgowski equations. In one embodiment of the invention a configuration is imparted to the entrance, exit, and side edges and faces of the magnet pole pieces as is shown in FIGS. 3, 4, 5 and 6. Providing such a shape ensures that the magnetic material magnetizes uniformly and that the flux distribution in the material remains constant at all magnetic field strengths. In general, the magnet of the present invention is applicable to the various known types of single focusing, magnetic mass spectrometers.

The present invention is also applicable to instruments generally referred to as double focusing mass spectrometers, i.e, analyzers that are capable of providing both an angular and an energy focus for heteroenergetic particles emitted by an ion source such as an electrical discharge source. A typical instrument is illustrated in FIG. 2 wherein a source of ions 28 is arranged to direct a particle beam at an electrostatic lens 30, which may be of either cylindrical or spherical type, with the partially sorted particles emerging from lens 30 being thereafter directed toward a deflecting and focusing magnet in sector 32 according to the present invention. Particles of a predetermined mass thereafter emerge from sector 32 and are collected at detector 34 located at the point of angular and energy focus for the analyzer. The detector is in turn connected to suitable readout electronics 36. As is typical of instruments of this type, a reversal of the positions of source 28 and detector 34 is also possible while still obtaining comparable operating results. The illustration in FIGS. 1 and 2 are representative of several possible sector angles for the magnetic analyzer according to the present invention. As shown, the magnet in FIG. 1, occupies an angular sector of approximately 120; the magnet in FIG. 2 occupies a sector of approximately 90. As shown, the entrance and exit ends form various angles with the longitudinal axis of the sector. Configurations other than straight line configurations are also possible. The use of a magnet having Rowgowski shaped pole pieces is likewise applicable to mass analyzers of other angular sectors, for example, an 180 sector type of instrument.

A specific embodiment of a magnet pole assembly according to the present invention is depicted in FIGS. 3 and 6. As shown therein the assembly comprises a pair of shaped, spaced pole pieces 42, 44 ofa magnetic material, e.g. vacuum cast pure iron such as that marketed under the designation Vacuumet, and having a predetermined configuration and profile, an entrance shunt assembly 38 disposed adjacent the entrance end 40 of the pair of pole pieces, and an exit shunt assembly 46 located adjacent the exit end of the pair of pole pieces. Shunt assembly 38 includes a pair of relatively thin, flat plates 48 of a magnetic material, a shunt holder 50 ofa non-magnetic material such as aluminum and a pair of shunt pieces 52, 54 located on opposite sides of assembly 38. Each of said spacers includes a length of nonmagnetic material such as aluminum approximately coextensive with the shunt holder in the longitudinal direction joined endwise to a length of magnetic material approximately coextensive with the magnetic shunt plates in the longitudinal direction. The magnetic material portion of the shunt spacersprovide the means whereby the magnetic circuit between the shunt plates is completed while at the same time providing a central opening between the plates to permit the entry and exit of charged particles at the magnetic analyzing sector.

Spacer 52 is secured to holder 50 by fastening means 51. Spacer 54 is secured to holder 50 by fastening means 53. Shunt plates 48 are secured to spacer 54 by fastening means 49. In a preferred embodiment the shunt assembly is attached to the ends of the pole pieces 42, 44 by an adhesive bond so as to not disturb the magnetic characteristics of the pole pieces. The

faces of the shunt holder adjacent the poles have a mating taper to permit a flush fit between the face of the shunt holder and the end faces 56, 58 of pole pieces 42, 44, respectively. The exit shunt assembly is similar in all respects to the entrance and shunt assembly and again comprises a pair of relatively thin plates of magnetic material 60 secured by suitable fastening means 62 to a non-magnetic shunt holder 64 with a pair of shunt spacers 66, 68 comprised of lengths of nonmagnetic and magnetic material joined endwise extending between the shunt holder and the shunts on opposite sides of the assembly. Spacer 66 is secured to holder 64 by fastening means 67. Spacer 68 is secured to holder 64 by fastening means 69. Shunt assembly 46 is, as before, secured to the exit end faces 70, 72 of poles 42, 44 by an adhesive bond.

The specific configuration and geometry of the sides and ends of poles pieces 42, 44 are best described with reference to FIGS. 4 and 5, section views taken through specified portions of the magnetic pole shown in FIG. 3. In FIG. 4, a section view taken along line 44 of FIG. 3, pole pieces 42, 44 are shown disposed such that pole faces 74, 76 are disposed in a facing relationship across a gap 78 of a predetermined width, the dimension of which will be referred to as having a measurement of a. In contrast to conventional magnetic pole pieces whose faces are normally machined square, the corners 80, 82 of pole piece 42 and corners 84, 86 of pole piece 44 are rounded with a predetermined radius proportional to the gap spacing, a, with the curvature extending between the straight lines defining pole faces 74, 76 and the straight lines defining side faces 88, 90, 92, 94, respectively. It will be noted that the side faces of both pole pieces taper outwardly with respect to the pole faces and have a predetermined slope. The overall thickness of pole pieces 42, 44, as measured along a perpendicular extending through pole faces 74, 76 and back faces 96, 98 as well as the width of the flat area on the pole faces between the curved edges, also hear a relation to overall performances of a magnet utilizing such poles.

The particular configuration of the end faces of pole pieces 42, 44 are illustrated by reference to FIG. 5, a section view taken along line 5-5 of FIG. 3. Entrance end faces 56, 58 shown in FIG. 5 are also illustrative of the configuration of exit end faces 70, 72, although said exit end faces are not specifically depicted in the drawing. As with the side corners, the end corners 100, 102 are rounded along an are having a predetermined radius. End faces 56, 58 likewise have an outward taper of a predetermined slope relative to a perpendicular to pole faces 74, 76.

Although first postulated for application to electrodes for creating a uniform electric field, the Rowgowski theory has been shown to be applicable to the shape of magnets used to create a uniform magnetic field. The generating mathematical expressions for the surface of the magnets according to the Rowgowski theory are y i a/rr(1r/2+ e where a is the minimum distance between the pole pieces (gap spacing) and d) is proportional to the magnetic flux between the pole pieces. The foregoing expressions define a pair of infinite exponential surfaces which to a satisfactory degree are approximately by pole pieces having a finite thickness and width. When applied to a magnet of high permeability the Rowgowski formula yields a structure characterized by essentially uniform magnetization throughout the pole pieces. In a presently preferred embodiment of the present invention, the exponential surfaces as defined by the Rowgowski equations above are approximated at the sides and ends of the pole pieces by two straight lines connected by a circular are having a radius of 1.25a. The first straight line corresponds to the pole face of each pole piece. The second straight line corresponds to the side end faces of the pole pieces and is connected to the arc such that the slope of the line corresponding to these side and end faces is ll.5. To complete the surfaces of the pole pieces a smooth transition between adjacent side and end faces is imparted thereto. To satisfactorily approximate the infinite Rowgowski surfaces and thereby obtain the desired objectives of uniform magnetization of the magnetic material and the flux distribution which remains constant at all field strengths, the thickness of the pole pieces according to a presently preferred embodiment is at least 3.3 33a and the width of flat area of the pole faces is at least 2.5a. An exact replica of the Rowgowski exponential surface can be imparted to the pole pieces by means of a computer operated machining programmed to follow the Rowgowski equations.

In order to be able to mathematically define the ion optics in an analyzer having a uniform magnetic field produced by magnets having the Rowgowski expontial shape, it has been found useful to employ shunts of magnetic material located near the entrance and exit faces of the magnet poles in the region of the fringing fields created by such poles. The specific location of the magnetic shunts with respect to the end faces of the pole pieces is a particular part of the present invention. It has been found that location of the shunts too closely adjacent the end faces of the poles may exert a loading effect on the poles creating a mathematically unpredictable edge effect, similar to the distortion produced when the square corners of conventional magnet poles go into saturation. According to the present invention the spacing of the magnetic shunts is approximately a distance 3.333a from both the entrance and exit end faces of the magnet poles.

A typical magnetic shunt plate 48 according to the present invention is illustrated in FIGS. 7A and 7B. As shown therein shunt plate 48 is approximately trapezoidal in plan view and is provided with a rounded edge L04 along the edge of the shunt most closely approaching the end faces of the pole pieces. In keeping with the basic function of the magnetic shunts or clamps to produce a sharp cutoff of the magnetic field, i.e., to precisely locate the field boundary, the thickness of the plate is determined by the requirement that the shunt have sufficient permeance to accommodate the intercepted flux in the fringing field. By spacing the magnetic shunts of the present invention a distance approximately 3.333a from the end faces, the objective of a sharp cutoff of the field is achieved without at the same time introducing any distortion or other indeterminate factors. The shunts also eliminate the aberrational effect of the field reversion which often occurs at a rela tively large distance away from the magnet particularly when the magnet yoke approaches or goes into saturation.

The improvement in performance in a small mass spectrometer utilizing shunted and shaped magnetic poles according to the present invention relative to the performance of a mass spectrometer of comparable size utilizing conventional shunted square poles is partially illustrated by reference to FIG. 8, a graph in which field strength in kilogauss (kg) in a magnetic analyzing sector is plotted along the ordinate and current in an electromagnetic coil generating the magnetic field is plotted along the abscissa. Curve 94 illustrates the performance of a conventional mass spectrometer. Curve 96 illustrates performance of a mass spectrometer according to the present invention. In the conventional mass spectrometer the useful upper limit of the magnetic field is typically 10 kg because it is at that point along the curve that significant distortion is encountered due to saturation effects at the square edges of the magnet. Thus despite the fact that it is possible to obtain higher field strengths with a conventional configuration, the operating range of the instrument is limited to the field strength shown. Operation beyond this limit is essentially meaningless since the distortion created in the magnetic analyzing field is such as to reduce the resolving power of the instrument.

In contrast, in a mass spectrometer according to the present invention, the flux distribution in the magnetic analyzing sector remains uniform regardless of the field strengths created in the sector. In one practical embodiment of an analyzer according to the present invention, the upper limit or maximum operating point is established at 20 kg.

Other advantages of a mass analyzer having poles according to the present invention are utilization of the discovery that magnetic reluctance of such poles is less than that for square poles of a comparable size. This is primarily due to the fact that square poles must carry a larger amount of flux in a direction perpendicular to the gap flux in order to supply magnetic flux to the fringing field. Thus in a square pole magnet the iron saturates with less gap flux than with exponentially shaped magnet poles. In terms of practical results, at least a 20 percent increase in gap flux density is achieved by utilizing magnetic poles according to the present invention.

By extending the working range of the magnet used with a high resolution mass spectrometer from l0 kg with square poles to 20 kg with exponentially shaped poles, the doubling of the working field strength means the provision of a mass spectrometer with four times the mass range. Alternatively, it is now possible to obtain four times as high an accelerating voltage for an equivalent mass thereby obtaining a significant increase in resolving power for the analyzer. Still another alternative way in which to employ the advantage of the present invention is the provision of a magnet of a substantially reduced size producing commensurate reductions in the size and cost of an analyzer utilizing such a magnet while still obtaining the same results as obtainable with prior high resolution square pole mass spectrometer. To the user of instruments of this type the improvement provides an instrument which has greatly simplified operating characteristics making such an instrument available for use by personnel with little or no familiarity with mass spectrometers while at the same time achieving operating results in terms of resolution in excess of that heretofore obtainable.

I claim;

1. A uniformly saturating electromagnet comprising:

a first pole half of a generally U-shaped configuration in both a transverse and longitudinal direction;

a second pole half of a generally U-shaped configuration in both a transverse and longitudinal direction spaced a predetermined distance from the first pole half, the two pole halves being aligned with the base portions of the U-shape facing each other in a parallel orientation, the side and end edges of the opposing base portions being rounded on a radius of approximately 1.25 times the distance between the pole halves and the arm portions of the U-shape being provided with an outward taper of a predetermined slope with respect to a perpendicular through the base portions; and

electric coil means associated with the pole halves in magnetic field generating relationship therewith.

2. A magnet according to claim 1 wherein the slope of the arm portions is approximately 1 3. A magnet according to claim 2 including magnetic shunting means for intercepting fringing flux lines associated with the magnet, the shunting means being located along the longitudinal axis of the pole halves and spaced a predetermined distance from the pole halves such that the flux distribution between the pole halves remains constant.

4. A magnet according to claim 3 wherein the magnetic shunting means comprises:

a first and second plate of a magnetic material and having a predetermined thickness disposed on opposite sides of a central area and spaced a distance approximately equal to the spacing of the pole halves;

first and second spacing means of a magnetic material located between the first and second plates and spaced apart a predetermined distance such that the plates and spacing means define an enclosed area;

a shunt holder of a non-magnetic material secured to the end faces of the pole halves such that the plates and spacing means are located a predetermined distance from the end faces; and

means for securing the plates and spacing means to each other and to the shunt holder.

5. A magnet according to claim 4 wherein the holder spaces the plates and spacing means a distance approximately 3.333 times the gap distance between the pole halves.

6. A magnet according to claim 5, wherein the thickness of the pole halves is at least 3.333 times the distance between the pole halves, and the width of the pole face is at least 2.50 times the distance between the pole halves. 

1. A uniformly saturating electromagnet comprising: a first pole half of a generally U-shaped configuration in both a transverse and longitudinal direction; a second pole half of a generally U-shaped configuration in both a transverse and longitudinal direction spaced a predetermined distance from the first pole half, the two pole halves being aligned with the base portions of the U-shape facing each other in a parallel orientation, the side and end edges of the opposing base portions being rounded on a radius of approximately 1.25 times the distance between the pole halves and the arm portions of the U-shape being provided with an outward taper of a predetermined slope with respect to a perpendicular through the base portions; and electric coil means associated with the pole halves in magnetic field generating relationship therewith.
 2. A magnet according to claim 1 wherein the slope of the arm portions is approximately 11.5*.
 3. A magnet according to claim 2 including magnetic shunting means for intercepting fringing flux lines associated with the magnet, the shunting means being located along the longitudinal axis of the pole halves and spaced a predetermined distance from the pole halves such that the flux distribution between the pole halves remains constant.
 4. A magnet according to claim 3 wherein the magnetic shunting means comprises: a first and second plate of a magnetic material and having a predetermined thickness disposed on opposite sides of a central area and spaced a distance approximately equal to the spacing of the pole halves; first and second spacing means of a magnetic material located between the first and second plates and spaced apart a predetermined distance such that the plates and spacing means define an enclosed area; a shunt holder of a non-magnetic material secured to the end faces of the pole halves such that the plates and spacing means are located a predetermined distance from the end faces; and means for securing the plates and spacing means to each other and to the shunt holder.
 5. A magnet according to claim 4 wherein the holder spaces the plates and spacing means a distance approximately 3.333 times the gap distance between the pole halves.
 6. A magnet according to claim 5, wherein the thickness of the pole halves is at least 3.333 times the distance between the pole halves, and the width of the pole face is at least 2.50 times the distance between the pole halves. 